82165682491200 has 4032 divisors, whose sum is σ = 401738787072000. Its totient is φ = 15943362969600.

The previous prime is 82165682491147. The next prime is 82165682491223. The reversal of 82165682491200 is 219428656128.

82165682491200 is a `hidden beast` number, since 8 + 2 + 1 + 6 + 56 + 82 + 491 + 20 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (4032).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 575 ways as a sum of consecutive naturals, for example, 50750883991 + ... + 50750885609.

It is an arithmetic number, because the mean of its divisors is an integer number (99637596000).

Almost surely, 2^{82165682491200} is an apocalyptic number.

82165682491200 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82165682491200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (200869393536000).

82165682491200 is an abundant number, since it is smaller than the sum of its proper divisors (319573104580800).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

82165682491200 is a wasteful number, since it uses less digits than its factorization.

82165682491200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1771 (or 1739 counting only the distinct ones).

The product of its (nonzero) digits is 3317760, while the sum is 54.

The spelling of 82165682491200 in words is "eighty-two trillion, one hundred sixty-five billion, six hundred eighty-two million, four hundred ninety-one thousand, two hundred".